About "mkdir") from macrumors/guides: http://guides.macrumors.com/mkdir
Strange that you mac creates a tmp-file (temporary file) on your desktop.
It seems something is seriously wrong - why does your Mac automatically create a directory by putting a file on your desktop? Strange...
Did you restore permissions on your harddisk and also TM-disk? - restart in recovery-mode by restarting using Command+R and then choosing Disk-repair and run it on those disks for best result.
If everything fails you could copy all of your important files to an external disk and go for a clean install...
I see no other solution.
I mailed "pondini" via his website a few hours ago...
He hasn't responded yet...
On his website he states: "I do not answer specific questions or problems via e-mail; only in the ASC forums",
- but I asked him anyway...
http://pondini.org/TM/Contact.html
Hi “pondini”,
Hope all is well…
Now macOS Sierra has arrived some people have Time Machine-troubles.
see thread (example) https://discussions.apple.com/thread/7677444?answerId=30688752022#30688752022&start=0&tstart=0
Hope to see you back in the Apple-forums.
You’re surely missed.
Compliments for all you have done in the past.
Sorry for my poor English.
Best regards,
Jur Kuipers, The Netherlands